Analytical approach while studying equations of boundary layer impulses at the flow in the inter-blade channel of gas turbines

Aeronautical and Space-Rocket Engineering

Thermal engines, electric propulsion and power plants for flying vehicles


DOI: 10.34759/vst-2021-1-45-60

Аuthors

Kishkin A. A.*, Zuev A. A.**, Delkov A. V.***, Shevchenko Y. N.****

Siberian State University of Science and Technology named after academician M.F. Reshetnev, 31, Krasnoyarsky Rabochy av., Krasnoyarsk, 660014, Russia

*e-mail: spsp99@mail.ru
**e-mail: dla2011@inbox.ru
***e-mail: delkov-mx01@mail.ru
****e-mail: gift_23j@mail.ru

Abstract

Severe requirements on energy and operation parameters are placed to the gas turbines’ air-gas channels designing.

Velocities distribution along the length of the interblade channel affects significantly the working body heat transfer to the structural elements, and velocity and pressure distribution profiles affect, in the first place, the temperature boundary layer profile distribution. It is essential to account for the specifics of the flow in the inter-blade channel, which represents a radial channel. Convoluted, non-closed lines of the flow with transverse pressure gradient, which significantly affect the slope of the flow bottom lines, and, correspondingly, the temperature boundary layer formation and transformation, are being realized in this radial channel.

Joint solution of the momentum and energy equations of the spatial boundary layer for the considered radial cavities of the inter-blade channel is necessary, which represents up-to-date scientific and engineering problem.

In [1, 2-4] the authors proposed analytical approach to hydrodynamic and thermal parameters determining in gas turbines’ rotation cavities with closed circular lines and transverse pressure gradient. However, the flow line is non-closed in the interchannel cavities, and solution of dynamics and energy equations is being significantly complicated.

The article considered the analytical approach to integrating momentum equations of the dynamic and spatial boundary layer for the flow-around surfaces of the curvilinear shape in the natural curvilinear system of coordinates with the presence of the transversal pressure gradient. The initial system of differential equations for the dynamic spatial boundary layer was integrated on the boundary layer thickness. As the result, a system of momentum equations in projections to the directions of natural coordinates was obtained.

The system of equations is presented in a more General form, in contrast to the already known solutions of G.Yu. Stepanov [6] and S.N. Shkarbul [7, 8], performed with account for the flow characteristics in the inter-blade channel of an axial turbine and along the cover disk of the impeller of a centrifugal pump, respectively. The suggested notation of the equation allows integrating in the case of the non-potential external flow over the surface of an arbitrary shape.

To solve the problem of the surface flow-around with account for the heat exchange, the joint solution of the obtained momentum equations and integral relation of energy of the temperature spatial boundary layer written in the natural curvilinear system of coordinates [5].

The resulting equations represent the parabolic type equations and require the finite-difference schemes application to solve them. To verify the obtained results, numerical studies of equations for the radial sector were performed.

Theoretical and experimental studies of the flow were performed in the radial sector (without accounting for the heat exchange) in the range of radii of Rmax = 0.169 m and Rmin = 0.031 m, at the flow angle of rotation from 0 to 90°. The flow velocity at the maximum radius varied within 5 ... 50 m/s, which corresponded to a change in the Reynolds number of ReU = 5.6•104...5.6•105.

Computational results are in satisfactory agreement with the results of these current lines visualization for the flow in the rectangular channel with cylindrical side walls along the circumferential guides.

Keywords:

dynamic boundary layer, momentum equations, inter-blade channel, air-gas channel of the turbo-pump unit, gas turbine

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